Story of Three persons blocked in a Cave

"Three persons of a people before you, were on a journey when they were overtaken by a storm and therefore they took shelter in a cave. A rock slipped down from the mountain and blocked the exit from cave.

One of them said: "The only way for deliverance left is to beseech Allah in the name of some virtuous deed." Thereupon one of them supplicated, "O Lord, my parents were very old, I used to offer them their nightly drink of milk before my children and the other members of the family. One day I went astray far away in search of green trees and could return only after my parent had gone to sleep. When I had milked the animals and brought their nightly drink to them, They were fast asleep, but I did not like to disturb them, nor would give any part of the milk to my children and other members of the family till after my parents had their drink. Thus, with the vessel in hand, I awaited their awakening till the flush of dawn, While the children cried out of hunger at my feet. When they woke up, they had their drink. O Lord, if I did this thing seeking only your pleasure, then do relieve us of the distress wrought upon us by this rock." Thereupon, The rock moved a little but that not enough to let them pass out.

Then the second man supplicated: "O Lord, I had a cousin whom I loved her more passionately than any loves a woman. I tried to seduce her but she would have none of me, till in a season of great hardship due to famine, she approached me (for help) and I gave her one hundred and twenty Dinars on condition that she would have sexual intercourse with me. She agreed, and when we got together and I was just going to have intercourse with her, she pleaded: 'Fear Allah, and do not break the seal unlawfully'; whereupon I moved away from her, despite the fact that I desired her most passionately; and I let her keep the money I had given her. O Lord, if I did this thing seeking only your pleasure, then do move the distress in which we find ourselves." Again the rock moved a little but not enough to let them pass out.

Then the third supplicated: "O Lord, I hired some laborers and paid them their dues, but one of them left leaving behind what was due to him. I invested it in business and the business prospered greatly." After a time the laborer came Back and said: 'O servant of Allah, hand over to me my wages.' I said to him: 'All that you see is yours - camels, cattle, goats and slaves.' He said: 'Don't play joke with me, O servant of Allah.' I assured him: 'I am mot joking.' So he took all of it sparing nothing. O Lord, If I did this seeking only for your pleasure, do relieve us of our distress."

The rock then moved away, and all the three came out of the cave safe and sound.

(Sahih Bukhari and Sahih Muslim )

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In the above hadith, the persons sought the tawassul by their good deeds.
Read the below authentic book for the permitted and prohibited formsof tawassul

Tawassul : Its types and Rulings - by Shaik Nasiruddin Albanee
The people are in great confusion about the matter of Tawassul and its rulings in the religion, and they greatly differ concerning it, some declaring it lawful and others prohibiting it, some going to extremes and other being over-lenient. Also, a large number of the Muslims have been used to saying in their supplications for centuries such things as: 'O Allah by the right of your Prophet …,' or by the right of the sacred house… forgive me.' `O Allah by the right of me Awliyaa and the pious, and so and so, etc.' Or `O Allah by the honor of the men of Allah to you, and by the honor of those in whose presence we are, and under whose assistance we exist, relief us and the distressed from all distress'… "So what is Tawassul? What are its types? What is the meaning of the Aayaat and the ahaadeeth, which mention it? And what is the correct ruling for it in Islam?"